Introduction

Seismic events with focal mechanisms located in the subducting slab are defined as “intraslab earthquakes”.

These events are often distributed along a double seismic zone (DSZ), defining an upper (0–10 km from the subduction interface) and a lower plane (more than 23 km from the subduction interface). Steady seismicity, i.e., excluding aftershocks of large events, has been observed between these two planes, defining interplane events (in between the upper and lower seismic planes, 10–23 km)1.

In the last decades, a number of scientific works examined the possible mechanisms responsible for their nucleation at intermediate depths (i.e., at depths of 70–300 km)2,3,4,5,6,7,8,9,10.

Fluids have been suggested to have an important role in triggering earthquakes in the subducting slab. In particular, the occurrence of metamorphic reactions involving dehydration of hydrous minerals in the crust (i.e., MORB dehydration) has been correlated to seismic episodes11,12,13,14,15,16 and, in particular, to seismicity peaks at 80 km depth1. As an example, in the DDST model (dehydration-driven stress transfer), antigorite breakdown has been invoked as responsible for intermediate depths seismicity in the subducting oceanic mantle14: in this model, obtained from studies on synthetic slightly serpentinized peridotite, the generation mechanism for intermediate-depth oceanic mantle earthquakes is related to the stress transfer from dehydrating antigorite portions to olivine portions in partially hydrated peridotite, as can occur in a network of serpentinized faults cutting fresh peridotite.

Dehydration embrittlement, after increasing fluid pressure in the oceanic lithosphere, has been proposed to trigger, above all, upper-plane and interplane earthquakes, including slow-slip events and episodic tremors close to the plate interface1,17,18,19. Fluid pressure can increase along preexisting faults, locally reducing their shear strength and triggering instabilities12,19,20. A rupture and a possible earthquake could also nucleate after the interaction, related to an increasing strain, of microcracks that formed from originally isolated pockets of water12,21. This mechanism would allow brittle failure to occur at greater depths than would normally be possible12.

Faccenda et al.22 showed that during slab deserpentinisation, unbending stresses could drive part of the released fluids downward into the cold core of the plate. These fluids can then percolate up-dip along a localized layer with zero slab-normal pressure gradients, which form together with the upper hydrated layer located near the top of the slab. The resulting double hydrated zone (DHZ) controls the locations where intermediate-depth seismicity could be triggered. The numerically predicted location and deformation mechanics of the DHZ appeared to be consistent22 with global seismological observations on DSZs23 and suggests that slab strength, lowering by percolating pressurized fluids, could be the viable mechanism for localization of the observed slab seismicity.

Other triggering mechanisms, such as shear heating or brittle failure due to stress amplification, exclude dehydration reactions: the first mechanism invokes the occurrence of thermal shear instabilities in the oceanic mantle; this hypothesis however requires high temperatures (more than 600 °C) and it thus cannot explain seismic events that occur at T < 600 °C1,3,24. Stress amplification is instead proposed to occur in slab domains characterized by inner rheological contrasts25. Local tectonics, bending stresses resulting from slab morphology, and the subduction rate may also control the pattern of intra-slab seismicity26,27.

Outer-rise faults (or bending faults) form in a prominent bathymetric bulge seaward of the trench axis, after the flexure of the subducting lithosphere; the incoming plate records the strongest bending within 50 km of the trench axis28,29,30. A direct correlation between outer-rise faults and intermediate earthquakes has been assumed by several authors31,32, according to which seismic events are derived from the reactivation of shallow incoming plate faults.

Boneh et al.8 identified a statistically significant positive correlation between a data set of intermediate‐depth global seismicity rates and the occurrence of shallow outer-rise normal faulting with large fault throw caused by plate bending. It has been therefore suggested that larger faults produce greater plate damage and a higher fluid circulation and hydration within the slab. As the result, the embrittlement of these intensely damaged and hydrated regions occurring at >70 km is in accordance with nucleation mechanisms for intermediate‐depth earthquakes.

On the other hand, Warren et al.33,34 found that the rupture directivity of intermediate‐depth earthquakes was inconsistent with the orientation of outer‐rise normal faults.

Recently, Gerya et al.35 demonstrated numerically that outer-rise normal faulting is a transient process, which leads to spontaneous segmentation of subducting slabs due to coupled brittle-ductile damage. Slab segmentation allowed to explain a number of subduction-related phenomena, including, in particular, the development of segmented seismic velocity anomalies in subducting slabs and the development of large offset normal faults at trenches35. According to the newly proposed slab segmentation theory, the maximal normal faults throw grows with time (Gerya et al.35, their Extended Data Fig. 6) and different subduction zones (or even different along-trench sections of the same subduction zone) can be characterized by different maturity of slab segmentation process and respectively by different magnitude of the maximal faults throw35. This is in apparent contradiction with the proposal of Boneh et al.8 that the maximal faults throw magnitude observed at the surface is representative of the entire subducting slab and controls the intermediate depth seismicity rate of the slab. This contradiction is intriguing and calls for further analyses.

Here, we build on these findings in order to test whether or not the proposed transient slab segmentation process35 can be reconciled with the observed positive correlation of the maximal outer rise faults throw and intermediate depth intra-slab seismicity rate8. Using our 2D numerical simulations of intraoceanic subduction, we demonstrate that many intraslab seismic events at intermediate depths (<200 km) could be correlated with transient episodes of stress increase within subducted intensely faulted and serpentinized slab segment boundaries. We moreover show that the stress increase occurs concurrently with either (i) transient outer-rise faults throw growth at the surface or (ii) transient episodes of interplate coupling.

Results

Outer-rise faults formation during subduction

The subduction process, which starts at the weak zone, evolves through time with the periodic formation of new faults in the slab, related to the flexure of the subducting oceanic lithosphere seaward of the trench axis.

Bending faults start to develop close to the trench: the main fault, with a dipping direction concordant to the subducting slab, generally develops taking advantage of pre-existing faults, even if it can also nucleate in the intact lithosphere. Secondary faults, concordant to the main fault, can form close to it. A set of antithetic faults later develops, finally forming a network of serpentinized faults in the subducting lithospheric mantle (Fig. 1).

Fig. 1: Some steps of the modeled intraoceanic subduction process, tracking the evolution of a new outer-rise faults network (reference model).
figure 1

a A main and antithetic serpentinized faults form in the oceanic lithosphere close to the trench. b The fault network enters the subduction zone and evolves in a graben-like structure. c–f Outer-rise faults are progressively buried at increasing depths while other faults develop at the surface. The lithologies are represented with different colors, as described in Supplementary Fig. 6. The red box highlights the evolution of the new fault network formed at the outer rise. White lines are isotherms (°C); “t” is the time after subduction begins. Here the main fault develops along a pre-existing fault.

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Main and antithetic faults propagate deeply in the lithospheric mantle till about 25 km from the upper surface of the oceanic crust, dislocating the oceanic crust in a sort of graben-like structure, with fault throw growing with time (Supplementary Fig. 1). Large-offset normal faults localize spontaneously into narrow intensively deformed zones thereby producing the progressive segmentation of the slab as highlighted by Gerya et al.35, with grain-size reduction being the key factor controlling this process35. The subduction evolves in a slab rollover geometry when the lithosphere interacts with the lower-mantle boundary, defined by the perovskite phase transition.

Fluids-free episodic deviatoric stress increase among subducted bending faults

We observed that the deformation along these faults is always coupled with deviatoric stress increase in lithospheric domains among the newly formed brittle structures (Fig. 2). As soon as faults form at shallow depths, generally deviatoric stress is maximum at the bottom of faults networks, close to the junction point of main and antithetic faults (Supplementary Fig. 2). With subduction progress, the regions of lithosphere among deforming bending faults record a transient, local, stress increase, with the strain being localized along main and secondary faults. When deformation along these structures stops, inter faults undeformed rock sectors are no longer solicited, and stress decreases, suggesting that the local transient stress increase among faults is strictly correlated with deformation along faults.

Fig. 2: Strain rate vs deviatoric stress in the reference model.
figure 2

Strain rate (Log(strain rate (s−1)); left column) is compared with deviatoric stress (Log(stress (Pa)); right column). The evolution of a new outer-rise fault network is highlighted with the purple box. During the formation of main and antithetic faults close to the trench, the strain rate along the fault zones is maximum (a), and stress is focused at the bottom joint point of these structures (b). Approaching the subduction zone, strain predominantly affects the main fault (c), and stress increase progressively affects wider volumes among faults (d). When a new fault network forms at the surface, strain affects both the subducted main and antithetic faults (e) and stress rises in inter-faults domains (f). With subduction progress, buried faults are only slightly deformed (g) and stress among them registers low values (h). The formation of new bending faults reactivates strain along the subducted faults (i) and inter-faults stress grows again (j).

Full size image

Episodes of transient stress increase in the slab are well visible following the fluctuation of deviatoric stress (Sii) in rock volumes among outer-rise serpentinized faults (Fig. 2b–j). Average deviatoric stress evolution with time in these rock volumes is shown in Fig. 3. In order to minimize the effects of local spurious stress oscillations characteristic to particle in cell methods with strong local viscosity variations36,37, we averaged deviatoric stress values over sufficiently large (50 × 50 km, i.e., 2500 grid cells, Fig. 2b–j) domains. We observed that several mechanisms can be responsible for spikes of average deviatoric stress in the slab during the subduction process:

Fig. 3: Plot of the mean value of the deviatoric stress.
figure 3

The mean value of deviatoric stress (Sii—Log (deviatoric stress (Pa)) recorded in an area around a selected bending fault network (e.g., small purple box in Fig. 2b–j) is plotted. Colored ovals depict stress spikes occurring concurrently either to the formation of new bending faults networks (2 and 3, green and blue ovals, respectively) or to episodes of interplate mechanical coupling (orange ovals).

Full size image

(a) slab unbending (7.25 My from subduction initiation) or bending (7.81 My from subduction initiation), simultaneous to the formation of new faults networks at the outer rise; in our models unbending occurs before the complete interaction of the slab with the lower-mantle boundary; after this interaction, unbending regions are confined within about 100 km-depth; on the other side the deeper parts of the subducted crust undergo bending, following the evolving rollover geometry of the slab (Fig. 4).

Fig. 4: Areas of overpressure and underpressure (Pa) in the reference model.
figure 4

Unbending (a, b) and bending stages (c) of the slab are pointed out. Slab at depths greater than about 100 km starts to bend after its interaction with the lower-mantle boundary (c).

Full size image

(b) Episodic and local coupling between the shallow mantle wedge and the subducting plate (7.28, 7.32, and 7.54 My) (Figs. 3 and 5): interplate mechanical coupling occurs after the subduction of an oceanic plate with a rugged surface, that is a consequence of the formation of outer-rise faults with a large offset, producing “graben-like” structures in the downgoing lithosphere. The increase of interplate coupling causes a temporary slow-down of subduction velocity and a simultaneous, very localized, increase of deviatoric stress by up to >1 GPa level within the very narrow coupling region.

Fig. 5: Coupling between the mantle wedge and the slab.
figure 5

a Deviatoric stress (Pa) showing mechanical coupling between the mantle wedge and the slab after the subduction of a large-throw graben, producing a stress build-up at the coupling region. Stress in slab region surrounding the subducted outer-rise faults is high compared to the other slab sectors. b Velocity along X direction (m s−1 *1e−9), with positive and negative values representing right-directed and left-directed movements, respectively. From 7.25 My till 7.32 My, the incoming plate records a velocity decrease related to the transient mechanical coupling between the upper mantle-wedge and the downgoing slab.

Full size image

The above mechanisms trigger a variation in the distribution of tectonic stress in the subducting plate that causes the increase of stress at outer-rise fault networks, which are the place of greater weakness of the subducting lithosphere.

The age of the plates (30 or 80 My vs 40 My of the reference model—Supplementary Figs. 3 and 4) does not strongly influence the stress behavior, since its increase, either in younger or older slabs, follows the same trend as in the reference model. This parameter, however, controls the depths inside the slab at which stress can increase: in older slabs (80 My), a buildup of the stress can occur even at 35 km from the slab surface, whereas in younger slabs (30 My) the stress can increase only till 25 km inside the slab. The age of the plates also affects the maximum temperature reached by serpentinized outer-rise faults: in older and colder slabs, in fact, faults reach a temperature slightly above 300 °C, whereas in younger oceanic lithosphere faults are confined by the 500 °C isotherm.

Discussion

Bending faults in nature

The evolution of bending faults and their role in subduction have been already examined through numerical models in previous works22,35,38,39,40. Moreover, the formation of bending faults and their role in arise alteration of the oceanic crust through the infiltration of water has been first postulated and then observed by several authors13,30,41,42,43,44,45,46,47,48. The high degree of alteration and fracturation in outer rise regions has been evidenced by a notable reduction of compressional wave velocities in the mantle at several convergent margins, although an alternative hypothesis has also been proposed49. For example, reduced velocities of the partially serpentinized mantle have been reported in subduction zones with little sediments such as Northern Chile46, Central Chile50, and Central America30,51, as well as in Southern Chile52. Local heat-flow anomalies also suggest that hydrothermal circulation is more vigorous where bend faults breach the seafloor and thus may govern fluid flow into the crust53. Indeed, it is widely accepted the valuable role of outer rise faults in allowing the transportation of fluids in the lithosphere and in the deep mantle through the geochemical alteration of faults rocks30,38,41,48,54,55,56,57,58.

It is well-known that the occurrence of fluids could support and enhance both fault reactivation, locally reducing their shear strength12,20, and causing cracking of intact rocks: isolated pockets of fluids hosted in rock pores can nucleate microcracks; increasing strain would cause the interaction of the microcracks to produce crack arrays, that would extend and coalesce21 and trigger rupture; the propagation of rupture through the water-filled microcracks would lead to substantial slip, stress drop and an earthquake12.

In our reference model, brittle failure propagates down to about 25 km from the top of the slab and is confined within the 500 °C isotherm. In nature, embrittlement can, however, occur at higher temperatures59, regardless of the presence of deep-water percolation48: several authors suggest, in fact, that the brittle/ductile transition becomes deeper within the subducting plate with increasing depth in the mantle and can occur at temperature even around 600–800 °C16,48. The temperature, at which brittle behavior can occur, seems controlled either by the age of the slab, in the presence of fluids (e.g., in a young slab brittle rheology could appear at a temperature greater than 500 ± 50 °C)22, or by the increase of the slab-pull forces (associated to the subduction of a relatively old, cold and heavy oceanic plate), even in a water-free environment48.

Moreover, we observed that the depths reached by stress buildup depend on the plate age: older slabs are characterized by stress increase affecting deeper parts of the subducted oceanic lithosphere compared to younger slabs. This is in accordance with what observed in most subduction zone23, where the distance between the upper and the lower planes of the DSZ increases with increasing slab age.

Dry outer-rise fault networks as sites for potential intermediate-depths earthquakes

In rock sectors undergoing a local stress increase, the occurrence of fluids released by dehydration reactions or preexisting fluids included in pores or microcracks could represent a contribution to reaching the brittle threshold of rocks, producing fracturing and possibly generating tremors or earthquakes.

The 2D simulations that we have run here show that the formation and the deformation of bending faults are accompanied by a local and transient increase of stress in lithosphere volumes surrounded by the newly formed fault network. In particular, we observed that this stress increase is strongly correlated with strain along serpentinized faults, i.e., stress increase occurs only when fault rocks are deformed and, therefore, re-activated by a perturbation given either by new bending faults formation or transient interplate coupling (Fig. 2).

Rock domains included in slab sectors among subducting bending faults, which are affected by transient stress increase, could represent volumes where potential rupture can occur, generating intraslab earthquakes, with/without the contribution of metamorphic reactions releasing fluids or mechanisms increasing fluid pressure. Indeed, the eventual occurrence of fluids in these domains could decrease the strength of already solicited rocks, promoting fracturing and eventual seismic events22. We propose that fracturing, faulting and intraslab earthquakes can occur, other than along main and secondary serpentinized faults, also in volumes among them. The possible role of fluids in this process22, cannot be evaluated with our simplified numerical model. Intermediate-depths earthquakes occurring in dry rock volumes have also been proposed by field-based observations10,60,61: as an example, Scambelluri et al.61 and Pennacchioni et al.62 found pseudotachylytes in dry lithospheric mantle domains banded by serpentinites, coherently exhumed from the eclogite facies conditions, testifying a seismic rupture occurring at intermediate depths.

We observed that stress build-up occurs during the formation of new bending fault networks at the outer rise or during episodic and local coupling between the shallow mantle wedge and the subducting plate; we, however, think that coupling, caused by structures on the subducting plate such as large-throw grabens, seamounts or oceanic plateau, could be only a secondary responsible for differential stress increase: it could be a very episodic mechanism, strongly related to the evolution of the morphology of the slab surface. Moreover, the volume of subducted sediments can play a major role in strongly influencing coupling: high sediment volumes at the subduction interface can, in fact, mask even a rugged morphology of the slab, inhibiting a possible interplate coupling and, thus, a build-up of the stress.

In general, earthquakes are expected to initiate in the cold core of the slab, where significant elastic stress can be maintained; rupture then propagates into a warmer, low-stress environment and this condition could be responsible for fault arrest63,64: near the nucleation patch the stress drop might be locally large, but it could gradually decrease and become locally negative as rupture propagates, producing a small spatially averaged stress drop65. Viscous weakening mechanisms, such as grain-size sensitive creep or flow of a melt layer, could possibly drive fault propagation in the slab64,66,67. As underlined by Turner et al.64, ruptures generating intermediate and deep earthquakes are mostly confined in regions where stress is potentially highest, with relatively low temperatures (lower than 1000 °C); this suggests that, regardless of their nucleation mechanisms, background stress exerts a first-order control on the propagation of intermediate and deep earthquakes, similar to what occurs for shallow earthquakes.

Moreover, it has been proven that, when across-strike fault interactions, other than, in example, regional tectonics, exert a stress-loading on faults, fault planes have more irregular stress patterns and interaction-influenced stress loading histories; the geometry of the fault/shear-zone system strongly controls stress-loading to failure in earthquakes68.

We, therefore, suggest that dry rock volumes in serpentinized fault networks, where stress transiently increases, could represent sectors of potential rupture, where earthquakes can easily nucleate even without the possible contribution of dehydration reactions or fluids overpressure, underlining the major role of fault interaction in regulating the slab stress pattern and earthquakes triggering. Our findings are thus in accordance with the above-mentioned field-based evidence and with what proposed by Toffol et al.25: using numerical modeling, they found that weak, circular-shaped flaws in the slab, which in nature could be represented by scattered serpentinized patches in meta-peridotite, behave as stress amplifiers in the strong dry slab. In these domains, high deviatoric stresses, compatible with earthquake nucleation at intermediate depth, are reached in the region of slab unbending. Many authors observed that also the shape and the orientation of the heterogeneity, with respect to the far-field stresses, exert an important influence on the concentration of stress69,70,71. In our simulations, outer-rise faults networks include serpentinized rocks (along the fault itself, with a general linear shape) that surround dry rock domains. The increase in deviatoric stress, that we observe in dry domains among serpentinized faults, could thus be ascribed to a sort of stress amplification process related to the rheological contrast between weak serpentinized faults and the dry lithospheric mantle of the subducting plate. The stress build-up in mantle rocks and their possible rupture, concomitant with strain increase along outer-rise faults that we observed, could be the result of flow of a weaker material surrounding dry strong volumes causing strain incompatibility across the deforming system, as has been observed in lower crustal rocks72,73 and in numerical models of subduction zone mélanges74.

The deep configuration of the slab in our simulations seems to partially influence the observed stress increase only in the mature stages of subduction (i.e., after the beginning of the interaction of the flattened leading edge of the slab with the underlying upper/lower mantle transition boundary) and only the deeper parts of the slab, since at least the shallower 100 km evolve independently and the fluctuation of stress values at outer-rise domains within this depth is independent of the evolution of the deep slab geometry.

The temporal coincidence of stress growth at intermediate depths and outer-rise faults throw growth at the trench, observed in our models, may also possibly explain the observed global positive correlation of intermediate-depth seismicity rate with maximal fault throw: what Boneh et al.8 observed in 17 subduction zones worldwide could represent the example in nature of our model steps in which we observe the gradual formation of outer-rise faults at the trench and the simultaneous intraslab stress increase at subducted slab segment boundaries. The intermediated-depth seismic activity that Boneh et al.8 correlate with a massive fluid occurrence at highly-fractured bending regions could thus be related also to mechanisms observed in our models, such as slab unbending/bending and interplate mechanical coupling.

Our interpretations are supported by observations of intermediate depths seismic activity in the Pacific slab under Japan75: it is found that intraslab earthquakes (magnitude 6.7–7.1) and their aftershock sequences generally occurred in lower seismic velocity zones within the subducting slab; these anomalies were attributed to heterogeneities in the slab and in particular to the occurrence of some pre-existing faults/fractures, where the dehydration of hydrous minerals, enhancing pore pressure increase, coupled with local tectonic and bending stresses, can cause intraslab events26. The analogy between lower-velocity zones and pre-existing faults/fractures within the slab was highlighted also by Gerya et al.35, which found that negative anomalies of velocity in the slab correspond to slab segment boundaries where outer-rise faults networks and grain-size reduction occur in some mature subduction zones.

The same behavior can be observed along some vertical cross-sections of P and S-wave tomography across northern Japan, where intraslab earthquakes focus preferably in slab portions affected by low-velocity anomalies (Supplementary Fig. 5): these regions could thus reflect the presence of serpentinized fractures and outer-rise faults, surrounding dry lithospheric mantle domains where stress build-up triggers seismic activity.

Methods

Numerical code specifications

The 2D numerical simulations shown here are based on the thermomechanical code I2VIS, which is built on the combination of a finite-difference method, applied on a staggered Eulerian grid, and a marker-in-cell technique76,77. The momentum, mass, and energy conservation equations are solved on the Eulerian grid, and physical properties are transported by Lagrangian markers. Non-Newtonian, viscoplastic rheologies and variable thermal conductivity are used in the model78,79 (Supplementary Table 1), which includes major phase transitions in the oceanic crust and mantle, plus adiabatic, radiogenic, and frictional internal heating sources. The full details of this method can be found in Gerya & Yuen76 and Gerya et al.35

Initial model setup

The initial model setup replicates a segment of an oceanic basin, where spontaneous subduction initiation occurs at a weak zone in the mantle with a prescribed size80,81. The simulated domain is 3000 × 3000 km along x and y directions (Supplementary Fig. 6), is resolved with an irregular rectangular grid of 1,261 × 511 nodes in the horizontal and vertical directions, respectively, and contains 19 million randomly distributed markers. The irregular grid resolution varies from 10 × 10 km at the model boundaries to 1 × 1 km in a 1000-km-wide and 200-km-deep subduction zone and outer-rise faulting area. Free-slip mechanical boundary conditions are applied to all sides of the model. A 12-km-thick ‘sticky’ air/water layer82 with low density (1 kg m−3 above 9 km, 1000 kg m−3 below 9 km) and viscosity (1017 Pa s) simulates the free-surface boundary condition atop the crust. Prescribing a laterally uniform cooling age and respective geotherm83 with 273 K at the surface and a mantle potential temperature of 1523 K, it is possible to reproduce the initial thermal structure and thickness of the plate (Supplementary Fig. 6).

In the reference model (maaj), the oceanic plates have a uniform age of 40 My. Two supplementary models explore subduction dynamics considering a uniform age of either 30 (maat) or 80 My (maaq), respectively. In the asthenospheric mantle, an adiabatic gradient of 0.5 K km−1 is initially prescribed (Supplementary Fig. 6).

In order to mimic the hot boundary layer at the core–mantle boundary, the temperature increases linearly by 744 K within 500 km at the lower boundary. For the mantle and the crust, a temperature-dependent thermal conductivity is used (Supplementary Table 1). The thermal boundary conditions at the top and at the bottom are 273 K and 3567–3717 K (depending on the mantle potential temperature), respectively, and zero heat flux on two other sides of the model.

The temperature of the ‘sticky’ air/water is kept constant at 273 K, in order to ensure efficient heat transfer from the surface of the crust. In the models, a gravitational acceleration of 9.81 m s−2 has been used.

Horizontal plate motion is simulated by applying a prescribed constant velocity (i.e., about 5 cm/y) to a narrow high-viscosity area prescribed in the incoming subducting plate.

Erosion and sedimentation processes shape the top of the lithosphere, according to the following Eulerian transport equation76:

$$\frac{\,\partial {z}_{{es}}}{\,\partial {{{{{\rm{t}}}}}}}=\,{v}_{z}-\,{v}_{x}\,\frac{\partial {z}_{{es}}}{\partial x}-\,{v}_{s}+\,{v}_{e},$$
(1)

where zes is the vertical position of the erosion/sedimentation surface as a function of the horizontal distance x, x, and z are horizontal and vertical coordinates, respectively, vs and ve are the sedimentation and erosion rates, respectively, vz and vx are the vertical and horizontal components of the material velocity vector at the surface, respectively. The sedimentation and erosion rates are the following84: vs  =  0 mm yr−1 and ve  =  0.3 mm yr−1 when z  <  9 km (the sea level prescribed in the model), and vs  =  0.03 mm yr−1 and ve  =  0 mm yr−1, when z  >  9 km. Considering the accumulated sedimentary prism, the maximal surface slope is limited by 17°. Surface processes have however, in our numerical experiments, a relatively minor role in subduction dynamics and slab morphology.

These models consider two oceanic plates, separated by a weak zone in the mantle. The oceanic crust consists of a 3 km-thick layer of basalts overlying a 5 km-thick layer of gabbroic rocks. No initial sedimentary layer is prescribed in the reference model. In these experiments, inherited faults affect the oceanic crust and the shallow lithospheric mantle till 14 km from the oceanic crust surface. Faults are 1 km thick and are 20 km spaced; where they affect the basaltic and gabbroic layers, they have a weak (basaltic) rheology, whereas, in the mantle, they are represented by serpentinitic rocks and have an inclination of about 63° toward the trench. Serpentinization of outer-rise fault networks occurs when the mantle rocks reach the upper strain limit (γ0). A serpentinite layer, 2 km thick, occurs at the base of the crust in the incoming plate, to simulate serpentinization of the mantle after the infiltration of fluids along inherited faults.

Density model

The extended Boussinesq approximation, with the incompressible continuity equation and variable density, has been implemented in the momentum and energy conservation equations. The following equation describes the variation of rock density with pressure (P) and temperature (T)

$$\rho_{P,T}={\rho }_{0}\,[1-\alpha (T-{T}_{0})][1+\beta (P-{P}_{0})],$$
(2)

where ρ0 is the standard density at P0 = 1 MPa and T0 = 298 K, and α = 2 × 10−5 Κ−1 and β = 4.5 × 10−12 Pa−1 are the coefficients of thermal expansion and compressibility, respectively (Supplementary Table 1).

We also considered the phase transformations of olivine into wadsleite and ringwoodite85 and into bridgmanite in the mantle86. The linear increase of density in the crust with pressure, from 0% to 16%, in the P–T region between the experimentally determined garnet-in and plagioclase-out phase transitions in basalt87 tries to reproduce the eclogitization of subducted basaltic and gabbroic crust. For density changes, stishovite and perovskite86 transitions in the crust are also taken into account.

Viscoplastic rheological model

The evaluation of the effective viscosity of the material allowed the implementation of viscous and brittle (plastic) properties in the models (Supplementary Table 1). For the ductile rheology, the contributions from different flow laws such as dislocation and diffusion creep are taken into account by composite rheology for ηductile:

$$\frac{1}{{\eta }_{{ductile}}}=\,\frac{1}{{\eta }_{{diff}}}+\,\frac{1}{{\eta }_{{disl}}}$$
(3)

where ηdiff and ηdisl are effective viscosities for diffusion and dislocation creep, respectively.

For the crust, constant grain size is assumed and ηdiff and ηdisl are computed as

$${\eta }_{{diff}}=\,\frac{A}{2{{{\sigma }}}_{{cr}}^{n-1}}{exp}\left(\frac{E+{PV}}{{{{{{\rm{RT}}}}}}}\right)$$
(4)
$${\eta }_{{disl}}= \frac{1}{2} {A}^{\frac{1}{n}}{\exp}\left(\frac{E+{PV}}{{{{{{\rm{nRT}}}}}}}\right) {\dot{\varepsilon}}_{{II}}^{\frac{1}{n}-1}$$
(5)

where T is the temperature (in K), P is pressure, R is the gas constant, ε̇II = \(\sqrt{1/2\left(\dot{\varepsilon }{{{{{\rm{ij}}}}}}\right)^2}\) is the square root of the second invariant of the strain rate tensor, σcr is the assumed diffusion–dislocation transition stress, and A, E, V, and n are the experimentally determined pre-exponential factor, activation energy, activation volume and stress exponent of the viscous creep, respectively (Supplementary Table 1).

Grain-size reduction and growth processes assisted by Zener pinning are also considered in the used ductile creep model for the mantle, and ηdiff and ηdisl are calculated according to references included in Gerya et al.35 The rheology follows a composite law as in Eq.(1), wherein:

$${\eta }_{{diff}}=\,\frac{1}{2}\,{A}_{{diff}}{h}^{m}{exp}\left(\frac{{E}_{{diff}}+P{V}_{{diff}}}{{{{{{\rm{RT}}}}}}}\right)$$
(6)
$${\eta }_{{disl}}=\,\frac{1}{2}\,{A}_{{disl}\,}^{\frac{1}{n}}{exp}\left(\frac{{E}_{{disl}}+P{V}_{{disl}}}{{{{{{\rm{nRT}}}}}}}\right)\,{\dot{\varepsilon}}_{{II}}^{\frac{1}{n}-1}$$
(7)

where h is the mean grain size and m is the grain-size exponent. The interplay between diffusion and dislocation creep is controlled by a grain-size-evolution equation dependent on the mechanical work and temperature. The grain-size evolution model is based on several assumptions. (1) Two well-mixed phases are present in the mantle peridotite: olivine and pyroxene, considered to have the same density and rheology, and have a fixed volume fraction of 60% and 40%, respectively. (2) In both phases, the relative motion is considered to be negligible, and therefore, their velocity is the same. (3) A self-similar log-normal distribution characterizes the grain-size distribution. Therefore, it always retains the same shape and its mean variance and amplitude are fully characterized by a unique grain size. (4) The system is in a state known as the pinned-state limit wherein the pinning of phases by each other controls the grain-size evolution (that is, Zener pinning is dominant)88. The grain size is thus controlled by the roughness r of the interface between the two phases. A relation between the mean grain size h (sufficient to fully describe the system) and the roughness r is given by h = \(\frac{r}{\sqrt{{h}_{g}}}\), where hg ≈ π/2 for the phase volume fraction in the models. The roughness evolution is described by the following equations88,89,90,91:

$$\frac{{{{{{\rm{dr}}}}}}}{{dt}}=\,\frac{\eta {G}_{1}}{q{r}^{(q-1)}}-\,\frac{{f}_{I}{r}^{2}}{{{{\gamma }}}_{I}\eta }{{\psi }}$$
(8)
$${G}_{I}=\,\frac{{G}_{g}}{{G}_{{fac}}}\,\frac{q}{p}\,{r}^{\left(q-p\right)}$$
(9)
$${G}_{g}=\,{A}_{g}{\exp}\left(\frac{{E}_{g}+P{V}_{g}}{{{{{{\rm{RT}}}}}}}\right)$$
(10)
$${f}_{I}=\,{f}_{0}{\exp}\left(-2{\left(\frac{T}{1,000}\right)}^{2.9}\right)$$
(11)

where GI is the interface coarsening, Gg is the grain growth rate, Gfac = 100 is the grain growth rate factor, p = 2 is the grain-size coarsening exponent, q = 4 is the roughness coarsening exponent, Ag = 2 × 10(4–6p) the is pre-exponential factor, γI is the surface tension, Eg = 3 × 105 is the grain-growth activation energy, Vg = Vdiff is the grain-growth activation volume, fI is the fraction of mechanical work Ψ converted to interface damage resulting in grain-size reduction; f0 = 0.001 is the interface damage at 1000 K, and η = 3φolφpx is interface area density depending on the volume fractions of olivine (φol = 0.6) and pyroxene (φpx = 0.4) in the mantle.

We implemented an effective viscous–plastic rheology combining ductile rheology with a brittle (plastic) rheology, where the following upper limit for the ductile viscosity is expressed as

$${\eta }_{{ductile}}{{\le }}\frac{C+{\mu }P}{2{{\dot{\varepsilon}}}_{{II}}}$$
(12)

μ = μ0 − γμγ for γ ≤ γ0 and μ = μ1 for γ > γ0,

$$\gamma =\int \sqrt{{{\frac{1}{2}}({\dot{\varepsilon}}_{{ij}({plastic})})^{2}}}{{{{{\rm{dt}}}}}}$$
(13)

In the above equations, μ is the internal friction coefficient, μ0 and μ1 are the initial and final internal friction coefficient, respectively (Supplementary Table 1), μγ = (μ0 − μ1)/γ0 is the rate of faults weakening with integrated plastic strain γ (γ0 is the upper strain limit for the fracture-related weakening), t is time, \({\dot{\varepsilon}}\) is the plastic strain rate tensor and C is the rock compressive strength at P = 0 (Supplementary Table 1). The mantle inside outer-rise normal faults that reached the upper strain limit (γ0) is serpentinized and has the respective rheology (Supplementary Table 1).

Deriving fault throw from numerical simulations

Integrated plastic strain γ stored on markers has been considered the base of fault throw estimation in our numerical models: we first defined a reference surface located inside the rheologically strong gabbroic layer at a 3.5-km vertical distance above the oceanic Moho, in order to have a conservative estimate of the plastic strain related to normal faulting. We later averaged, at the nearest vertical grid lines intercepting this reference surface, strain on markers which were found within 250-m vertical distance around the reference surface. Faults are therefore defined by the local maxima of the plastic strain γ, for which an effective fault throw magnitude M was calculated as:

$$M=\gamma D\sin (\alpha )$$
(14)

where D = 1 km is a characteristic fault width in our models (as faults always localize within one grid cell) and α is the normal fault dip angle in the models. As the sensitivity threshold for this numerical approach, we have used a throw of 20 m.

Other specifics of model design and the numerical code are provided by Gerya et al.35